Work done in time $t$ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time $t_1$ as a function of time $t$ is given by
$\frac{1}{2}m\,\frac{v}{{{t_1}}}{t^2}$
$m\,\frac{{{v}}}{{{t_1}}}{t^2}$
$\frac{1}{2}{\left( {\,\frac{{mv}}{{{t_1}}}} \right)^2}{t^2}$
$\frac{1}{2}m\,\frac{{{v^2}}}{{{t^2}_1}}{t^2}$
A bag of sand of mass $M$ is suspended by a string. A bullet of mass $m$ is fired at it with velocity $v$ and gets embedded into it. The loss of kinetic energy in this process is
A cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is
Two bodies of masses $m_1$ and $m_2$ are moving with same kinetic energy. If $P_1$ and $P_2$ are their respective momentum, the ratio $\frac{P_1}{P_2}$ is equal to
A ball of mass $m$ is dropped from a heigh $h$ on a platform fixed at the top of a vertical spring, as shown in figure. The platform is depressed by a distance $x.$ Then the spring constant is
A sphere is suspended by a thread of length $\ell $. What minimum horizontal velocity has to be imparted to the sphere for it to reach the height of the suspension